After setting the “Debug” option when saving (and code-signing) the app, it does work, meaning that it opens in debug mode, and I can step through the code.

However, display alert and display dialog do not open the alert/dialog, and I have to kill the execution to get control back. This is unfortunate, because I have to test the remaining script, depending on the dialog/alert’s answer.

Do I miss something, or is that behavior to be expected?

A temporary fix is to deactivate the alsert/dialog and to hard set the answer.

Probably sounds silly but might the dialogs be appearing behind the ScriptDebugger window? We often run into this issue with our apps in general unless we specify an activate to bring it to the front. Would be worth moving the SD window when you expect a dialog to be interacting with.